Application of Double Beltrami states to solar eruptions

Abstract

We show that the general class of Double Beltrami (DB) states, which are the lowest energy equilibria of Hall magnetohydrodynamics, can have characteristics similar to those of active regions in the solar corona and is capable of undergoing a catastrophe that can cause a solar eruption, such as a flare or coronal mass ejection (CME). We then show that the qualitative evolution of the DB state is consistent with that of a solar eruption. Finally, we make two quantitative comparisons of DB states to CMEs, which are the simplest result of the catastrophe. First, we show that the DB expansion by a factor of 1–2 before the catastrophe is consistent with the increase in the height of the leading edges of Large‐Angle Spectrometric Coronagraph (LASCO C1) CMEs in the quasi‐equilibrium stage. Secondly, we use the assumption that DB states are randomly chosen from the allowed phase space of coronal structures to predict that the probability of a coronal structure erupting is 0.046. Identifying active regions with DB states and using observational constraints to estimate that the state is replaced every 60 min by emerging loops results in a CME rate of 11 d−1, which is in reasonable agreement with the actual rate of about 6 d−1 at solar maximum.

Beltrami–Bernoulli equilibria in weakly rotating self-gravitating fluid

“…This implies equilibrium states in self-gravitating fluid are also endowed with two length scales in a gravitomagnetic field. This can have major consequences for the formation of large-and small-scale flow configurations in the fluid as demonstrated in charged fluid (Mahajan et al 2001;Kagan & Mahajan 2010).…”

On Beltrami states near black hole event horizon

“…On the other hand, these Beltrami states can also terminate because of changes (via reconnection or other non-ideal effects) in field topology. For example, in solar physics, a class of states known as Double Beltrami (DB) states, the superposition of two force free states, is shown to have the characteristics similar to those of active regions in the solar corona [32][33][34]. The breakdown of these DB states in those active regions can lead to catastrophic eruptive events such as coronal mass ejections (CME).…”

Double Beltrami states and loss of equilibrium in electron, positron and ion plasmas

“…Hence, the solutions of force-free magnetic fields have been employed to model diverse phenomena occurring in the solar atmosphere such as solar flares (Mahajan et al. 2002; Kagan & Mahajan 2010), solar coronal loops (Bhattacharyya et al. 2007; Fuentes-Fernández, Parnell & Hood 2010), solar mass ejections, coronal heating (Mahajan et al.…”

“…At lowest order, the non-magnetic forces can be neglected and the magnetic field becomes force free as the Lorentz force vanishes. Hence, the solutions of force-free magnetic fields have been employed to model diverse phenomena occurring in the solar atmosphere such as solar flares (Mahajan et al 2002;Kagan & Mahajan 2010), solar coronal loops (Bhattacharyya et al 2007;Fuentes-Fernández, Parnell & Hood 2010), solar mass ejections, coronal heating (Mahajan et al 2001;Browning & Van der Linden 2003;Hood, Browning & Van der Linden 2009) and magnetic clouds (Burlaga 1988;Hidalgo, Nieves-Chinchilla & Cid 2002) etc. Recently, have modelled astrophysical outflows employing the unified dynamo-reverse dynamo mechanism which is based on the simultaneous generation of the flows and field using Hall double Beltrami fields.…”